王健泽 email ： [email protected] preliminary investigations on post-earthquake assessment of...

王健泽 Email ： [email protected]

Preliminary Investigations on Post-earthquake Assessment of Damaged RC Structures Based on Residual Drift

Jianze WangSupervisor: Assoc. Prof. Kaoshan Dai

State Key Laboratory of Disaster Reduction in Civil Engineering

May 2015

The 5th Tongji-UBC Symposium on Earthquake Engineering

[email protected]


Outline

Background and Motivations

Seismic assessment methods based on residual drifts

Application to E-Defense shaking table model

Discussion and Conclusion


1.Background and motivations

Performance-based Assessment

Performance Indicators

Roof driftInterstory drift(GB. FEMA-356, ATC-58,Eurocode-8….)

Element deformationDamage Indices (e.g. Park & Ang)…………..


1.Background and motivations

Roof driftInterstory drift(GB. FEMA-356, ATC-58, Eurocode-8….)

Maximum drift took place during earthquake

0 5 10 15 20 25 30-300

-200

-100

0

100

200

300

400

Dis

pla

cem

en

t(m

m)

Time(s)

Unknown after main-shock

Residual drift

Maximum displacement

Residual displacement

Measurable


2.Seismic assessment methods based on residual drifts

a). Empirical Relations between Maximum and Residual drifts

b). Probabilistic Estimation

………….


2.Seismic assessment methods based on residual drifts a). Empirical Relations

(Hatzigeorgiou et.al, 2011)𝑢𝑚𝑎𝑥=(𝑎1𝑇+𝑎2𝑢𝑟𝑒𝑠+𝑎3𝑢𝑟𝑒𝑠2 +𝑎4𝑇 𝑢𝑟𝑒𝑠)×(1+𝑎5 𝐻+𝑎6 𝐻

2)

(Zhang et.al,2013)

(Garcia, 2006)

(Takeda) (Kinematic)

d𝑅=d𝑇𝑃

[−0.069 𝑎g2 +1.164𝑎g ]× 102𝑟+3.58

(Gong et.al,2011)

………….


2.Seismic assessment methods based on residual drifts b). Probabilistic estimation (Yazgan and Dazio, 2012)

Step 1:

Modeling of the structure Step 2:

Estimation the prior probabilistic distribution of the maximum drift ratio Step 3:

Updating the maximum drift ratio distribution based on visible damage Step 4:

Updating the maximum drift ratio distribution based on known residual drift


3.Application to E-Defense shaking table model A full-scale four-story RC structure model(Design and instrumentation of the 2010 E-Defense Four-Story Reinforced Concrete and Post-Tensioned Concrete Buildings, Peers, 2011)

Longitudinal Direction (X) : Moment frame system

Transverse Direction (Y): Frame-Shear wall system

Story Height: 3m;

Overall Height: 12m;

All data were download from

https://nees.org/warehouse/filebrowser/1005


3.Application to E-Defense shaking table model A full-scale four-story RC structure model

Ground motions: JMA-Kobe motions (1995) , scaled by 25%, 50%, 100%

Excitation Input

X direction

Displacements (mm) Drifts

Maximum Residual Maximum Residual

KOBE-25% 22 0.2 0.184% 0.001%

KOBE-50% 141 2.6 1.181% 0.022%

KOBE-100% 272 9.6 2.269% 0.080%

Table. Roof displacements after each scenario

0 1 2 3 4 5 60

5

10

15

20

25

30Absolute Acceleration Spectra

Tn(s)

PG

A(m

/s2)

Kobe-25%Kobe-50%Kobe-100%

0 10 20 30 40 50 60-6

-4

-2

0

2

4

6

8

Acc

ele

ratio

n(m

/s2 )

Time(s)



(Hatzigeorgiou et.al, 2011)𝑢𝑚𝑎𝑥=(𝑎1𝑇+𝑎2𝑢𝑟𝑒𝑠+𝑎3𝑢𝑟𝑒𝑠2 +𝑎4𝑇 𝑢𝑟𝑒𝑠)×(1+𝑎5 𝐻+𝑎6 𝐻

2)

(Zhang et.al,2013)

(Garcia, 2006)

(Takeda) (Kinematic)

d𝑅=d𝑇𝑃

[−0.069 𝑎g2 +1.164𝑎g ]× 102𝑟+3.58

(Gong et.al,2011)

………….

Method: a) Empirical Relations

Eq.1

Eq.2

Eq.3

Eq.4

Eq.5



Calculation result (mm) Difference

Eq.1 54.2 80%Eq.2 16.1 94%Eq.3 38.5 86%Eq.4 70.5 74%Eq.5 140 49%

Method: a) Empirical Equtions

In JMA-Kobe-100% test, the maximum roof displacement(drift) is 272mm(2.26%) in X direction

With the equations, the results are:


10 15 20 25 30 35 40

-2

-1

0

1

2

x 10-3

Tims(s)

Ro

of

Dri

ft

TestSimulation

10 15 20 25 30 35 40-0.015

-0.01

-0.005

0

0.005

0.01

0.015

Tims(s)

Ro

of

Dri

ft

TestSimulation

10 15 20 25 30 35 40

-0.02

-0.01

0

0.01

0.02

Tims(s)

Ro

of

Dri

ft

TestSimulation

Method: b) Probabilistic Estimation3.Application to E-Defense shaking table model

Step 1:Modeling of the structure Perform-3D Nonlinear simulation:

• Beam: plastic hinges at member ends Column: fiber sections• Actual material properties obtained

from specimen in tests• Cyclic degradation and strength loss

were considered

Kobe-25%-X

Kobe-50%-X

Kobe-100%-X

Comparisons between tests and simulations


3.Application to E-Defense shaking table model Method: b) Probabilistic EstimationStep 2: Estimation the prior probabilistic distribution of the maximum drift ratio

Earthquake Name

Year Station Name Mw Rjb (km)

Rrup (km)

Vs30 (m/sec)

Kobe Japan

1995 KJMA 6.9 0.94 0.96 312

Assumption: Certainties: Structure propertiesUncertainties: Ground motions

One structure model

A set of 50 ground motion records(PEER-NGA database, http://peer.berkeley.edu/nga/)

Prior probabilistic distribution:


3.Application to E-Defense shaking table model Method: b) Probabilistic EstimationStep 2: Estimation the prior probabilistic distribution of the maximum drift ratio

0 1 2 3 4 5 60

10

20

30

40

50

60

70

Tn(s)

PG

A(m

/s2)

Sa(T=0.68,ζ 0.05)=1.91g＝

0 1 2 3 4 5 60

5

10

15

20

25

30

35

40

Period,T(sec)

Sa

(cm

/s2)

Sa(T=0.68s,ξ=0.05)=1.22g)

0 1 2 3 4 5 60

5

10

15

20

25

30

35

40

45

50

Tn(s)

PG

A(m

/s2)

Sa(T=0.68s)

Uncertainties extent:

Case 1: A reliable record is available. (JMA-Kobe) Sa(T1,ζ=0.05) of JMA-Kobe

Sa(T1,ζ=0.05) of 50 records

Case 2: MCE Response spectrum is available (USGS)Sa(T1,ζ=0.05) of spectrum

Sa(T1,ζ=0.05) of 50 records

Case 3: Just fundamental properties of the seismic event are known.(Mw, Rjb, Site….)GMPM model (Attenuation relationship)(Campbell and Bozorgnia, 2007)

Median:0.82gσln(Sa)=0.58


3.Application to E-Defense shaking table model Method: b) Probabilistic EstimationStep 3: Updating the maximum drift ratio distribution based on visible damage

Damage description: (After JMA-Kobe-100%)

2.5mm shear crack width in interior beam-column joints

1.1mm shear crack width in exterior beam-column joints

250mm height of cover concrete spalled in first story(Nagae et.al, 2012)


Assume uniform distribution : Updated maximum drift ratio distribution:

3.Application to E-Defense shaking table model Method: b) Probabilistic EstimationStep 3: Updating the maximum drift ratio distribution based on visible damage

ElementType

Structural Performance Levels

Collapse Prevention Life Safety Immediate Occupancy

Primary

Extensice cracking and hinge formation in ductile elements. Limited cracking

and/or splice failure in some nonductile columns. Severe damage in short

columns

Extensive damage to beams. Spalling of cover and shear

cracking (<0.32mm) for ductile columns. Minor spalling in nonductile columns. Joint

cracks <0.32mm wide.

Minor hairline cracking. Limited yielding possible

at a few locations. No crushing (strains below

0.003).

Secondary

Extensive spallings in columns and beams. Severe joint damage.

Some reinforcing buckled.

Extensive cracking and hinge formation in ducttile elements. Limited cracking and/or splice

failure in some nonductile columns. Severe damage in

short columns.

Minor spalling in a few places in ductile columns

and beams. Flexural cracking in beams and

columns. Shear cracking in joints<0.16mm.

Drift 4% transient 2% transient 1% transient

Performance levels taken from FEMA-356


Step 4: Updating the maximum drift ratio distribution based on known residual drift

Pr ( M 𝑖∩ R 𝑗|𝐼 )=Pr ( 𝐼|𝑀 𝑖∩ R 𝑗 ) Pr

(M ¿¿ 𝑖∩ R 𝑗)

∑𝑖∑𝑗

Pr ( 𝐼|𝑀 𝑖∩ R 𝑗 ) Pr (M ¿¿ 𝑖∩ R 𝑗)¿¿

3.Application to E-Defense shaking table model Method: b) Probabilistic Estimation

Joint probability of max and residual drift given on visible damage:

0.250.5

0.751

1.251.5

1.752

2.252.5

2.753

3.253.5

3.75

0.10.2

0.30.4

0.5

0

1

2

3

4x 10

-3

Maximum drift ratio,da,m

[%]

Residual drift ratio,da,r [%]

Pro

ba

bili

ty

Case 3:

0.250.5

0.751

1.251.5

1.752

2.252.5

2.753

3.253.5

3.75

0.10.2

0.30.4

0.5

0

0.5

1

1.5

2x 10

-3

Residual drift ratio,da,r

[%]Maximum drift ratio,da,m [%]

Case 1:

0.250.5

0.751

1.251.5

1.752

2.252.5

2.753

3.253.5

3.75

0.10.2

0.30.4

0.5

0

1

2

3x 10

-3

Maximum drift ratio,da,r

[%]Residual drift ratio,d

a,r [%]

Case 2:


1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 3.25 3.5 3.75 4 0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Maximum average drift ratio,da,m

[%]

Pro

ba

bili

ty

P(Mi)

P(Mi|I)

P(Mi|(IMR)

Test:2.26%

3.Application to E-Defense shaking table model Method: b) Probabilistic Estimation

1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 3.25 3.5 3.75 4 0

0.05

0.1

0.15

0.2

0.25

Maximum drift ratio,da,m

[%]

Pro

ba

bili

ty

P(Mi)

P(Mi|I)

P(Mi|(IMR)

Test:2.26%

Prior distribution

Updated distribution based on visible damage

Updated distribution based on residual drift

Roof Drift After JMA-Kobe-100% X directionTest: 2.26%Estimation (Maximum Probability):

Case 1: in the range 2.25%-2.5%

Case 2: in the range 2%-2.25%

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 3.25 3.5 3.75 4 0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Maximum average drift ratio,da,m

[%]

Pro

ba

bili

ty

P(Mi)

P(Mi|I)

P(Mi|(IMR)

Test:2.26%

Case 3: in the range 2.75%-3%


0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

500

1000

1500

2000

Ba

se S

he

ar(

kN)

Roof Drift(%)

Intact SPOQuadrilinear ApproxDamaged SPOQuadrilinear Approx

Unload at 2.5% and reload

=0.94%

3.Application to E-Defense shaking table model Residual roof drift Maximum roof drift Post-earthquake assessment

(Residual seismic capacity Sa,cap)

Pushover for intact and damaged structures

With the help of SPO2IDA spreadsheet tool, IDA curves could be derived.(Vamvatsikos amd Cornell, 2002.)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

0.5

1

1.5

2

2.5

3

Sa(T

1)

Roof Drift(%)

IDA-INTACTIDA-DAMAGEDIDA-DAMAGED(with residual drift)

IDA curves


Structure Sa,cap(T1)(g)INTACT 2.93

DAMAGED 2.04DAMAGED

(considered residual drift)2.86

Seismic capacity Sa,cap(T1) (Median,50th)

Aleatory uncertainty (βR): 0.45Epistemic uncertainty (βU): 0.40

3.Application to E-Defense shaking table model

Fragility Curves：

0 1 2 3 4 5 60

0.2

0.4

0.6

0.8

1

Sa(T

1)(g)

Pro

ba

blit

y

16th

Median(50th)

84th


4.Discussion and Conclusion

1. Empirical relations between maximum and residual drift derived from

simulations are unapplicable to result of the E-Defense shaking table

test. The dispersion of residual drift should be considered.

2. Probabilistic estimation could predict the maximum roof drift more

accurately if residual roof drift and visible damage are available.

3. In order to get better assessment results, the uncertainties of structure

and ground shaking should be evaluated and quantified reasonably.

4. The maximum drift distribution of structural damage used in step 3 of

probabilistic estimation should be developed to a more accurate model.


Thanks

王健泽 email ： [email protected] preliminary investigations on post-earthquake assessment of...

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